On Coding by (2,q)-Distance Fibonacci Numbers

Abstract

In 2006, A. Stakhov introduced a new coding/decoding process based on generating matrices of the Fibonacci p-numbers, which he called the Fibonacci coding/decoding method. Stakhov's papers have motivated many other scientists to seek certain generalizations by introducing new additional coefficients into recurrence of Fibonacci p-numbers. In 2013, I. Wloch et al. studied (2,q)-distance Fibonacci numbers F-2(q,n) and found some of their combinatorial properties. In this paper, we state a new coding theory based on the sequence (T-q(n))(n=-infinity)(infinity), which is an extension of Wloch's sequence (F-2(q,n))(n=0)(infinity).